System and method for determining amount of radioactive material to administer to a  patient

ABSTRACT

In one embodiment, a computerized system and method are provided for determining an optimum amount of radioactivity to administer to a patient, comprising: assuming an activity retention limit; utilizing the activity retention limit to determine a dose rate for a phantom category; utilizing the dose rate for the phantom category to determine the dose rate for a second phantom category; and utilizing the dose rate for a second phantom category to find information regarding the second phantom category. In other embodiments, a computerized system and method are provided for determining an optimum amount of radioactivity to administer to a patient, comprising: obtaining at least one image relating to anatomy of a particular patient; obtaining multiple images regarding radioactivity distribution over time in the particular patient; combining the radioactivity images with the anatomy images; running a Monte Carlo simulation to obtain dose image information; and using the dose image information to obtain BED and/or EUD information.

This application claims priority to provisional application 60/860,315filed on Nov. 21, 2006 and also to provisional application 60/860,319,filed on Nov. 21, 2006. Both provisional applications are hereinincorporated by reference.

This invention was made with Government support under NIH/NCI grantR01CA116477 and NIH/NCI grant R01CA116477 and DOE grantDE-FG02-05ER63967. The authors also acknowledge. The U.S. Government hascertain rights in this invention.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates a method for determining an amount of radioactivematerial to administer to a patient, according to one embodiment.

FIG. 2 illustrates different types of models that can be used indetermining dose rates for patients.

FIGS. 3-4 illustrate examples of actual images of patients.

FIG. 5 illustrates the output of a 3D-RD calculation, according to oneembodiment.

FIG. 6 lists example reference phantom parameter values.

FIG. 7 provides example 48 h whole-body activity retention values fordifferent phantoms and F₄₈ values.

FIG. 8 illustrates DRC values for different F₄₈ values.

FIG. 9 depicts examples of administered activity limits for differentphantoms and F₄₈ values as a function of T_(E) when T_(RB) is set to 20h.

FIG. 10 depicts example corresponding results when T_(RB) equals 10 h.

FIG. 11 depicts examples of absorbed dose to lungs as a function ofT_(E) for different F₄₈ values.

FIG. 12 depicts example results for the different phantoms at F₄₈=0.9when DRC=20 cGy/h.

FIGS. 13A and 13B illustrates absorbed dose v. T_(E) curves for adultfemale phantom and for two different remainder body effective clearancehalf-lives.

FIG. 14 illustrates a method for a 3D-RD calculation, according to oneembodiment.

FIG. 15A illustrates an example of computed tomography (CT) images; FIG.15B illustrates an example of positron emission tomography (PET) images;and FIG. 15C illustrates an example of kinetic parameter images.

FIGS. 16-20 illustrates the use of EUD and BED formulas, according toseveral embodiments.

FIGS. 21-22 illustrates various parameter values.

FIG. 23 illustrates an example of how an outer shell (with 2 hour halflife) is separated from an inner sphere (with 4 hour half life).

FIG. 24 illustrates an example of the impact of dose distribution onEUD.

FIGS. 26A-D illustrate various image.

FIG. 27 depicts an example of the DVH of the absorbed dose distributionobtained with 3D-RD, according to one embodiment.

FIGS. 28 and 29 depict example results obtained with the radiobiologicalmodeling capabilities of 3D-RD, according to several embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION Utilizing ActivityRetention Limit to Obtain Dose Rate

FIG. 1 illustrates details on how an activity retention limit isutilized to obtain the dose rate, according to one embodiment. Theresulting dose rate (also referred to as absorbed dose rate) can, forexample, make it possible to account for patient-specific differences indetermining dose rates for patients. By moving to a dose-rate instead ofan activity-based limit on the treatment prescription it is possible toapply well-established and clinically validated constraints on therapyto situations that differ from the original studies used to define theselimits. It is also possible to consider the impact of combined, externalradiotherapy with targeted radionuclide therapy in determining theoptimal amount of radioactivity to administer to a patient. Once adose-rate has been obtained, it is easier to use many available datasets to assist the patient. The following data sets are examples of datasets that can be utilized: Press et al., A Phase I/II Trial ofIodine-131-Tositumomab (anti-CD20), Etoposide, Cyclophosphamide, andAutologous Stem Cell Transplantation for Relapsed B-Cell Lymphomas,Blood, Volume 96, Issue 9, Pages 2934-42 (2000); Emami et al., Toleranceof Normal Tissue to Therapeutic Irradiation, Int. J. Radiation. Oncol.Biol. Phys., Volume 1991, Issue 21, pages 109-122. Those of ordinaryskill in the art will see that many other data sets can also beutilized.

Choose Activity Retention Limit

In 105, an activity retention limit is chosen or assumed. This activityretention limit can be assumed based on data sets, such as theBenua-Leeper studies or other studies that have determined the maximumtolerated dose in a patient population. The Benua-Leeper studies haveproposed a dosimetry-based treatment planning approach to ¹³¹I thyroidcancer therapy. The Benua-Leeper approach was a result of theobservation that repeated ¹³¹I treatment of metastatic thyroid carcinomawith sub-therapeutic doses often fails to cause tumor regression and canlead to loss of iodine-avidity in metastases. The Benua-Leeper studyattempted to identify the largest administered ¹³¹I radioactivity thatwould be safe yet optimally therapeutic. Drawing upon patient studies,the Benua-Leeper study formulated constraints upon the administeredactivity. For example, the Benua-Leeper study determined that the bloodabsorbed dose should not exceed 200 rad. This was recognized to be asurrogate for red bone marrow absorbed dose and was intended to decreasethe likelihood of severe marrow depression, the dose-limiting toxicityin radioiodine therapy of thyroid cancer. In addition, it was determinedthat whole-body retention at 48 h should not exceed 120 mCi. This wasshown to prevent release of ¹³¹I-labeled protein into the circulationfrom damaged tumor. Furthermore, in the presence of diffuse lungmetastases, it was determined that the 48 h whole-body retention shouldnot exceed 80 mCi. This constraint helped avoid pneumonitis andpulmonary fibrosis. Thus, for example, referring to FIG. 1, in 105, an80 mCi activity retention limit at 48 h can be assumed based on theBenua-Leeper studies. As shown below, the 48 hr retention limit isconverted to a dose-rate limit that can then be used to adjust the 80mCi to a value that would deliver the same dose-rate for differentpatient geometries (e.g, pediatric patients)

Determine Dose-Rate in Reference Phantom

In 110 of FIG. 1, utilizing the activity retention limit chosen in 105,S-factors for different phantoms are used to convert the activityretention limit to a dose-rate DRQ). In equation (1) below, a dose-rateDR(t) for lungs at time t in reference phantom P is found:

DR ^(P)(t)=A _(LU)(t)·S _(LU←LU) ^(P) +A _(RB)(t)·S _(LU←RB) ^(P)  (1).

with:

$\begin{matrix}{{{A_{LU}(t)} = {\frac{A_{T} \cdot F_{T}}{^{{- \pi_{LU}} \cdot T}}^{{- \lambda_{LU}} \cdot t}}},} & (2) \\{{{A_{RB}(t)} = {\frac{A_{T} \cdot \left( {1 - F_{T}} \right)}{^{{- \lambda_{RB}} \cdot T}}^{{- \lambda_{RB}} \cdot t}}},} & (3) \\{{S_{{LU}\leftarrow{RB}}^{P} = {{S_{{LU}\leftarrow{TB}}^{P} \cdot \frac{M_{TB}^{P}}{\left( {M_{TB}^{P} - M_{LU}^{P}} \right)}} - {S_{{LU}\leftarrow{LU}}^{P} \cdot \frac{M_{LU}^{P}}{\left( {M_{TB}^{P} - M_{LU}^{P}} \right)}}}},} & (4)\end{matrix}$

A_(LU)(t) lung activity at time t,|

S_(LU←LU) ^(P) lung to lung ¹³¹I S-factor for reference phantom, P,

A_(RB)(t) remainder body activity (total-body-lung) at time, t,

S_(LU←RB) ^(P) remainder body to hung ¹³¹I S-factor for referencephantom, P,

A_(T) whole-body activity at time, T,

F_(T) fraction of A_(T) that is in the lungs at time, T,

λ_(LU) effective clearance rate from lungs (=ln(2)/T_(E); withT_(E)=effective half-life),

λRB effective clearance rate from remainder body (=ln(2)/T_(RB), withT_(RB)=effective half-life in remainder body),

S_(LU←TB) ^(P) total-body to lung ¹³¹I S-factor for reference phantom.P,

M_(TB) ^(P) total-body mass of reference phantom. P,

M_(LU) ^(P) lung mass of reference phantom. P.

Equation (2) describes a model in which radioiodine uptake intumor-bearing lungs is assumed instantaneous relative to the clearancekinetics. Clearance is modeled by an exponential expression with aclearance rate constant, λ_(LU), and corresponding effective half-life,T_(E). At a particular time, T, after administration, the fraction ofwhole-body activity that is in the lungs is given by the parameter,F_(T). Activity that is not in the lungs (i.e., in the remainder body(RB)) is also modeled by an exponential clearance (Equation (3)), butwith a different rate constant, λ_(RB). At time, T, the fraction ofwhole-body activity in this compartment is 1-F_(T). Equation (4) can beobtained from the following reference: Loevinger et al., MIRD Primer forAbsorbed Dose Calculations, Revised Edition., The Society of NuclearMedicine, Inc. (1991).

Using equations (2) and (3) to replace A_(LU)(t) and A_(RB)(t) inequation 1, the dose rate to lungs at time, T, for phantom, P, is:

DR ^(P)(T)=A _(T) ·F _(T) ·S _(LU←LU) ^(P) +A _(T)·(1−F _(T))·S _(LU←RB)^(P)  (5).

Derived Activity Constraint

In 115, once we have the dose-rate at a certain time (e.g., 48 h) as therelative constraint for a certain phantom, then dose-rate constraints(DRCs) at this same time (e.g., 48 h) can be derived for differentreference phantoms. Thus, for example, If we assume that the dose-rateto the lungs at 48 h is the relevant constraint on avoiding prohibitivelung toxicity, then, one may derive 48-hour activity constraints fordifferent reference phantoms that give a 48 h dose rate equal to apre-determined fixed dose rate constraint, denoted, DRC. By re-orderingexpression 5 and renaming A_(T) to A_(DRC) ^(P), the activity constraintfor phantom P so that DR^(P)(48 h)=DRC, we get:

$\begin{matrix}{A_{DRC}^{P} = {\frac{DRC}{{F_{48} \cdot S_{{LU}\leftarrow{LU}}^{P}} + {\left( {1 - F_{48}} \right) \cdot S_{{LU}\leftarrow{RB}}^{P}}}.}} & (6)\end{matrix}$

In equation 6, A_(DRC) ^(P), depends upon the fraction of whole-bodyactivity in lungs at 48 hours and also on the reference phantom thatbest matches the patient characteristics.

Corresponding Administered Activity

In 120, once we have the dose rate constraints for different phantoms,corresponding administered activity can be found for those phantoms.Equation (6) gives the 48 hour whole-body activity constraint so thatthe dose rate to lungs at 48 hours does not exceed DRC. Thecorresponding constraint on the maximum administered activity, AA_(max),can be derived by using equations 2 and 3, to give an expression for thetotal-body activity as a function of time:

$\begin{matrix}{{A_{TB}(t)} = {{\frac{A_{T} \cdot F_{T}}{^{{- \lambda_{LU}} \cdot T}}^{{- \lambda_{LU}} \cdot t}} + {\frac{A_{T} \cdot \left( {1 - F_{T}} \right)}{^{{- \lambda_{RB}} \cdot T}}{^{{- \lambda_{RB}} \cdot t}.}}}} & (7)\end{matrix}$

Replacing A_(T) with A_(DRC) ^(P) and setting t=0, the followingexpression is obtained for

AA_(max):

$\begin{matrix}{{A\; A_{\max}} = {\frac{A_{DRC}^{P} \cdot F_{48}}{^{{- \lambda_{\omega}} \cdot 48}} + {\frac{A_{DRC}^{P} \cdot \left( {1 - F_{48}} \right)}{^{{- \lambda_{RB}} \cdot 48}}.}}} & (8)\end{matrix}$

The denominator in each term of this expression scales the activity upto reflect the starting value needed to obtain A_(TB) (48 h)=A_(DRC)^(P). AA_(max) is shown to be dependent on λ_(LU), and λ_(RB) (orequivalently on T_(E) and T_(RB)).

Mean Lung Absorbed Dose

In 125, the mean absorbed dose may be obtained by integrating the doserate from zero to infinity. Thus, the mean lung absorbed does can beobtained by integrating equation (1) from 1 to infinity:

DLU=Ã _(LU) ·S _(LU←LU) ^(P) +Ã _(RB) ·S _(LU←RB) ^(P)  (9).

Integrating the expressions for lung and remainder body activity as afunction of time, (equations (2) and (3), respectively) and replacingparameters with the 48 hour constraint values the following expressionsare obtained for Ã_(LU) and Ã_(RB):

$\begin{matrix}{{{\overset{\sim}{A}}_{LU} = {\frac{A_{DRC}^{P} \cdot F_{48} \cdot ^{\frac{\ln {(2)}}{T_{E}}T}}{\ln (2)} \cdot T_{E}}},} & (10) \\{{\overset{\sim}{A}}_{RB} = {\frac{A_{DRC}^{P} \cdot \left( {1 - F_{48}} \right) \cdot ^{\frac{\ln {(2)}}{T_{RB}} \cdot T}}{\ln (2)} \cdot {T_{B}.}}} & (11)\end{matrix}$

In equations (10) and (11), the λ values have been replaced toexplicitly show the dependence of the cumulated activities on theclearance half-lives.

If T_(RB) is kept constant and T_(E) is varied, the minimum absorbeddose to the lungs will occur at a T_(E) value that gives a minimum forequation (9). This can be obtained by differentiating with respect toT_(E), setting the resulting expression to zero and solving for T_(E).This gives T_(E)=ln(2)·48 h=33 h.

Electron v. Photon Contribution to the Lung Dose

Since almost all of the activity in tumor-bearing lungs would belocalized to tumor cells, it is instructive to separate the electroncontribution to the estimated lung dose from the photon contribution.The electron contribution would be expected, depending upon the tumorgeometry (11), to irradiate tumor cells predominantly, while the photoncontribution will irradiate lung parenchyma. The dose contribution fromthe remainder body is already limited to photon emissions. The photononly lung to lung S-value (S_(LU←LU) ^(P)) for a phantom, P, is obtainedfrom the S-factor value and the delta value for electron emissions of¹³¹I:

$\begin{matrix}{{{SP}_{{LU}\leftarrow{LU}}^{P} = {S_{{LU}\leftarrow{LU}}^{P} - \frac{\Delta_{electron}^{\,^{131_{I}}}}{M_{LU}^{P}}}},} & (12)\end{matrix}$

Δ_(electron) ¹³¹ ^(I) Total energy emitted as electrons perdisintegration of ¹³¹I. Replacing SP^(P) _(LU←LU) for S^(P) _(LU←LU) inequation 9 gives the absorbed dose to lungs from photon emissions only.

Parameter Values

The table in FIG. 6 lists the reference phantom parameter values used inthe calculations. The masses, lung-to-lung and total body-to-lungS-values listed were obtained from the OLINDA dose calculation program.The remainder body (RB)-to-lung and lung-to-lung photon-only S valueswere calculated using equations (4) and (12), respectively. Theeffective clearance half-life of radioiodine activity not localized tothe lungs, T_(RB), was set to 10 or 20 h. These values correspond toreported values for whole-body clearance with or without recombinantTSH, respectively. The effective clearance half-life for activity intumor-bearing lungs, T_(E), was varied from 20 to 100 h. The fraction ofwhole-body activity in the lungs at 48 h, F₄₈, was varied from 0.6 to 1.

EXAMPLE

To derive the dose-rate to lungs associated with the 80 mCi, 48 hconstraint we assume that 90% of the whole-body activity is uniformlydistributed in the lungs (F₄₈=0.9). The original reports describing the80 mCi, 48 h limit do not provide a value for this parameter; the valuechosen is consistent with the expected biodistribution in patients withdisease that is dominated by diffuse lung metastases. As noted above,the 80 mCi activity constraint was derived primarily from resultsobtained in females. Accordingly, the conversion from activity todose-rate is performed using S-factors and masses for the adult femalephantom. Using equation, (5), with F₄₈=0.9, the dose-rate constraint(DRC) corresponding to the 48 h, 80 mCi limit is 41.1 cGy/h. This is theestimated dose-rate to the lungs when 80 mCi of ¹³¹I are uniformlydistributed in the lungs of an adult female whose anatomy is consistentwith the standard female adult phantom geometry. Implicit in the 80 mCiat 48 h constraint is that radiation induced pneumonitis and pulmonaryfibrosis will be avoided as long as the dose-rate is not in excess of41.1 cGy/h at 48 h after ¹³¹I administration. If we assume that thisdose-rate based constraint applies to pediatric patients, then usingequation 6, we may calculate the 48 h activity limitation if the patientanatomy is consistent with the 15 or 10 year-old standard phantom. FIG.7 provides the 48 h whole-body activity retention values for differentphantoms and F₄₈ values. Since the guidelines were developed with datafrom females, the 80 mCi rule applied to adult males gives a 48 hwhole-body activity constraint of 3.73 GBq (101 mCi) at F₄₈=0.9;corresponding values for the 15-year old and 10-year old phantoms are2.46 GBq (66.4 mCi) and 1.73 GBq (46.7 mCi). It is important to notethat because it is a dose-rate, DRC, does not depend upon the clearanceparameters. The value chosen, does, however, depend upon the assumedlung fraction of whole-body activity. FIG. 8 lists the DRC values fordifferent F₄₈ values. All of the results presented will scale linearlyby DRC value.

The majority of patients with diffuse ¹³¹I-avid lung metastases exhibitprolonged whole-body retention. In such cases, the whole-body kineticsare dominated by tumor-associated activity. Assuming that 90% of thewhole-body activity is in the lungs and that this clears with aneffective half-life of 100 h, while the remainder activity clears withan effective half-life of 20 h (corresponding to a treatment plant thatincludes hormone withdrawal), equation (8) may be used to calculate theadministered activity that will yield the corresponding 48 h activityconstraint for each phantom. The administered activity values are 6.64,5.23, 4.37 and 3.08 GBq (180, 143, 118 and 83.2 mCi), respectively, foradult male, female, 15 year old and 10 year old standard phantomanatomies. These values depend on the assumed clearance half life ofactivity in the remainder of the body. If an effective half-life of 10 h(consistent with use of recombinant human TSH (rhTSH)) is assumed, thecorresponding administered activity values are: 15.1, 12.0, 9.92 and6.98 GBq (407, 323, 268 and 189 mCi). FIG. 9 depicts administeredactivity limits for different phantoms and F₄₈ values as a function ofT_(E) when T_(RB) is set to 20 h. FIG. 10 depicts corresponding resultswhen T_(RB) equals 10 h. The plots show that at T_(E) greater than threeto four times T_(aRB) the administered activity limit is largelyindependent of lung clearance half-life but, as shown by the equidistantspacing of the curves with increasing F₄₈, remains linearly dependent onthe fraction of whole-body activity that is in the lungs at 48 h. WhenT_(E) approaches the lower T_(RB) value as in FIG. 9, AA_(max) increasesrapidly and appears to converge. This reflects the condition of apartitioned activity distribution that clears from lungs and remainderbody at the same effective half-life; the AA values at T_(E)=T_(RB)=20 hare not the same because the dose-rate, which is used to determineAA_(max) will be different due to the physical distribution of theactivity even when the half-lives are the same. The rapid increase inAA_(max) at lower T_(E) values reflects the need to increase patientadministered activity as the clearance rate increases.

FIG. 11 depicts the absorbed dose to lungs as a function of T_(E) fordifferent F₄₈ values. Since the administered activities are adjusted toreach a constant 48 h dose-rate in lungs, the absorbed dose curves areessentially independent of phantom geometry with less than 2% differencein lung absorbed dose vs T_(E) profiles across the 4 standard phantomgeometries (data not shown). Both sets of curves show a minimum absorbeddose at T_(E)=33.3 h (=ln(2)×48 h). The minimum absorbed dose is 53.6 Gyfor T_(RB)=20 h and ranges from 53.6 (F₄₈=1) to 54.2 Gy (F₄₈=0.6) forT_(RB)=10 h.

Less is known regarding the effects of lung irradiation on pediatricpatients or patients with already compromised lung function. In suchcases a more conservative dose-rate limit may be appropriate. As notedearlier, the results shown in FIGS. 7, and 9-11 scale linearly with DRC,the table in FIG. 12 summarizes the relevant results for the differentphantoms at F₄₈=0.9 when DRC=20 cGy/h. In the adult female phantom, thiscorresponds to 1.44 GBq (38.9 mCi) retained in the whole body at 48 h.

All of the lung absorbed dose values shown on FIG. 11 and listed in thetable in FIG. 12 are well above the reported 24 to 27 Gy MTD for adultlungs. The discrepancy may be explained by considering the photon andelectron fraction of this absorbed dose. The electron emissions aredeposited locally, most likely within the thyroid carcinoma cells thathave invaded the lungs, while the photon contribution would irradiatethe total lung volume. Using equations (9) and (12), the lung absorbeddose attributable to photons may be calculated. Absorbed dose vs T_(E)curves are depicted in FIGS. 13A and 13B for the adult female phantomand for the two different remainder body effective clearance half-livesconsidered. The photon absorbed dose is less dependent upon clearance oflung activity (i.e., T_(E)) and more dependent on remainder bodyclearance. Comparing FIG. 13A with FIG. 13B, there is a greater thantwo-fold increase in the photon absorbed dose as the clearance rate isdoubled and F₄₈=0.6. The increase depends upon the spatial distributionso that at F₄₈=0.9, the dose increases by a factor of 1.6.

Unlike the total dose, the photon dose is also more heavily dependentupon the phantom. At T_(E)=100 h, the photon lung dose to the adult maleranges from 8.75 (F₄₈=1.0) to 9.03 (F₄₈=0.6) Gy when T_(RB)=20 h; thecorresponding values when T_(RB)=10 h, are 8.75 (F₄₈=1.0) and 9.56(F₄₈=0.6) Gy. In the 15-year-old, the corresponding values are: 7.85,8.10, 7.85 and 8.55 Gy; corresponding values for the 10-year-old are:7.09, 7.33, 7.09 and 7.78 Gy.

3D-RD (3D-Radiobiological Dosimetry)

In one embodiment, a method is provided that incorporatesradiobiological modeling to account for the spatial distribution ofabsorbed dose and also the effect of dose-rate on biological response.The methodology is incorporated into a software package which isreferred to herein as 3D-RD (3D-Radiobiological Dosimetry).Patient-specific, 3D-image based internal dosimetry is a dosimetrymethodology in which the patient's own anatomy and spatial distributionof radioactivity over time are factored into an absorbed dosecalculation that provides as output the spatial distribution of absorbeddose.

FIGS. 3-4 illustrate actual images of patients. FIG. 5 illustrates theoutput of a 3D-RD calculation. FIG. 14 sets forth a method for a 3D-RDcalculation. Referring to FIG. 14, in 1405, anatomical images of thepatient are obtained. For example, one or more computed tomography (CT)images, such as the images illustrated in FIG. 15A, one or more singlephoton emission computed tomography (SPECT) images, such as the imagesillustrated in FIG. 15B, and/or one or more positron emission tomography(PET) images can be input. A CT image can be used to provide density andcomposition of each voxel for use in a Monte Carlo calculation. A CTimage can also be used to define organs or regions of interest forcomputing spatially averaged doses. For example, a CT image can show howa tumor is distributed in a particular organ, such as a lung. Alongitudinal series of PET or SPECT images can be used to perform avoxel-wise time integration and obtain the cumulated activity or totalnumber of disintegrations on a per voxel basis. If multiple SPECT or PETstudies are not available, a single SPECT or PET can be combined with aseries of planar images. By assuming that the relative spatialdistribution of activity does not change over time, it is possible toapply the kinetics obtained from longitudinal planar imaging over atumor or normal organ volume to the single SPECT or PET image, therebyobtaining the required 3-D image of cumulated activity. The results ofsuch a patient-specific 3-D imaging-based calculation can be representedas a 3-D parametric image of absorbed dose, as dose volume histogramsover user-defined regions of interest or as the mean, and range ofabsorbed doses over such regions. Such patient-specific, voxel-basedabsorbed dose calculations can help better predict biological effect oftreatment plans. The approach outlined above provides estimated totalabsorbed dose for each voxel, collection of voxels or region. Analternative approach that makes it easier to obtain radiobiologicalparameters such as the biologically effective dose (BED) is to estimatethe absorbed dose for each measure time-point and then perform thevoxel-wise time integration to get the total absorbed dose delivered.This approach makes it easier to calculate dose-rate parameters on a pervoxel basis which are needed for the BED calculation.

In 1408, images are obtained relating to radioactive distribution acrosstime.

FIG. 15C illustrates an example of kinetic parameter images; in thiscase the effective half-life for each voxel is displayed in acolor-coded image. These kinetic parameter images provide an estimate ofclearance rate of the radiological material in each voxel in a 3D image.

In 1410, the images related to the radioactive distribution areregistered across time. At this point, one of at least two options(1415-1440 or 1450-1465) can be followed. In 1415, each radioactivityimage can be combined with an anatomy image. The anatomical image voxelvalues can be utilized to assign density and composition (i.e., water,air and bone).

In 1420, Monte Carlo simulations are nm on each activity image. Thus,the 3-D activity image(s) and the matched anatomical image(s) can beused to perform a Monte Carlo calculation to estimate the absorbed doseat each of the activity image collection times by tallying energydeposition in each voxel.

In 1425, the dose image at each point in time is used to obtain adose-rate image and a total dose image.

In 1430, the dose-rate and the total dose image are utilized to obtainthe BED image. In 1440, the BED image is utilized to obtain the EUD ofBED value for a chosen anatomical region.

In the other option, after 1410, activity images can be integratedacross time voxel-wise to obtain a cumulated activity (CA) image. In1455, the CA image is combined with an anatomy image. In 1460, a MonteCarlo (MC) calculation is run to get the total dose image. In 1465, thedose image is utilized to obtain the EUD of the dose value for a chosenanatomical region.

EUD and BED formulas (as described in more detail below and alsoillustrated in FIGS. 16-20) can be utilized to incorporate theradiological images into the anatomical image(s). The spatial absorbeddose distribution can be described by the equivalent uniform dose (EUD,defined on a per structure basis). The rate at which the material isdelivered can be described by the biologically effective dose (BED,defined on a per voxel basis).

EUD and BED

The uniformity (or lack thereof) of absorbed dose distributions andtheir biological implications have been examined. Dose-volume histogramshave been used to summarize the large amount of data present in 3-Ddistributions of absorbed dose in radionuclide dosimetry studies. TheEUD model introduces the radiobiological parameters, α and β, thesensitivity per unit dose and per unit dose squared, respectively, inthe linear-quadratic dose-response model. The EUD model converts thespatially varying absorbed dose distribution into an equivalent uniformabsorbed dose value that would yield a biological response similar tothat expected from the original dose distribution. This provides asingle value that may be used to compare different dose distributions.The value also reflects the likelihood that the magnitude and spatialdistribution of the absorbed dose is sufficient for tumor kill.

It is known that dose rate influences response. The BED formalism,sometimes called Extrapolated Response Dose, was developed to comparedifferent fractionation protocols for external radiotherapy. BED may bethought of as the actual physical dose adjusted to reflect the expectedbiological effect if it were delivered at a reference dose-rate. As inthe case of EUD, by relating effects to a reference value, this makes itpossible to compare doses delivered under different conditions. In thecase of EUD the reference value relates to spatial distribution and ischosen to be a uniform distribution. In the case of BED the referencevalue relates to dose rate and is chosen to approach zero (total dosedelivered in an infinite number of infinitesimally small fractions).

As described above with respect to 1415, the patient-specific anatomicalimage(s) are combined with radioactivity images into paired 3D datasets. Thus, the anatomical image voxel values can be utilized to assigndensity and composition (i.e., water, air and bone). This information,coupled with assignment of the radiobiological parameters, α, β, μ, theradiosensitivity per unit dose, radiosensitivity per unit dose squaredand the repair rate assuming an exponential repair process,respectively, is used to generate a BED value for each voxel, andsubsequently an EUD value for a particular user-defined volume.

In external radiotherapy, the expression for BED is:

$\begin{matrix}{{B\; E\; D} = {{{Nd}\left( {1 + \frac{d}{\alpha/\beta}} \right)}.}} & (1)\end{matrix}$

This equation applies for N fractions of an absorbed dose, d, deliveredover a time interval that is negligible relative to the repair time forradiation damage (i.e., at high dose rate) where the interval betweenfractions is long enough to allow for complete repair of repairabledamage induced by the dose d; repopulation of cells is not considered inthis formulation but there are formulations that include this and thiscould easily be incorporated in embodiments of the present invention.The parameters, α and β are the coefficients for radiation damageproportional to dose (single event is lethal) and dose squared (twoevents required for lethal damage), respectively.

A more general formulation of equation (1) is:

BED(T)=D _(T)(T)·RE(T)  (2),

where BED(T) is the biologically effective dose delivered over a time T,D_(T)(T) is the total dose delivered over this time and RE(T) is therelative effectiveness per unit dose at time, T. The general expressionfor RE(T) assuming a time-dependent dose rate described by D(t) is givenby:

$\begin{matrix}{{R\; {E(T)}} = {1 + {\frac{2}{{D_{T}(T)}\left( \frac{\alpha}{\beta} \right)} \times {\int_{0}^{T}\ {{{t} \cdot {\overset{.}{D}(t)}}{\int_{0}^{t}\ {{{w} \cdot {\overset{.}{D}(w)}}{^{- {\mu {({t - w})}}}.}}}}}}}} & (3)\end{matrix}$

The second integration over the time-parameter, w, represents the repairof potentially lethal damage occurring while the dose is delivered,i.e., assuming an incomplete repair model. If we assume that the doserate for radionuclide therapy, D(t), at a given time, t, can beexpressed as an exponential expression:

{dot over (D)}(t)={dot over (D)} ₀ e ^(−A1)  (4),

Where D₀ is the initial dose rate and λ is the effective clearance rate(=ln(2)/t_(e); t_(e)=effective clearance half-life of theradiopharmaceutical), then, in the limit, as T approaches infinity, theintegral in equation (3) reduces to:

$\begin{matrix}{\frac{{\overset{.}{D}}_{0}^{2}}{2\; {\lambda \left( {\mu - \lambda} \right)}}.} & (5)\end{matrix}$

Substituting this expression and replacing D_(T)(T) with D, the totaldose delivered, and using D₀=λD , which may be derived from equation(4), we get:

$\begin{matrix}{{B\; E\; D} = {D + {\frac{\beta \; D^{2}}{\alpha}{\left( \frac{\ln (2)}{{\mu \cdot t_{e}} + {\ln (2)}} \right).}}}} & (6)\end{matrix}$

In this expression, the effective clearance rate, λ, is represented byln(2)/te. The derivation can be completed as discussed in the followingreferences: Dale et al., The Radiobiology of Conventional Radiotherapyand its Application to Radionuclide Therapy, Cancer Biother Radiopharm(2005), Volume 20, Chapter 1, pages 47-51; Dale, Use of theLinear-Quadratic Radiobiological Model for Quantifying Kidney Responsein Targeted Tadiotherapy, Cancer Biother Radiopharm, Volume 19, Issue 3,pages 363-370 (2004).

In cases where the kinetics in a particular voxel are not well fitted bya single decreasing exponential alternative, formalisms have beendeveloped that account for an increase in the radioactivityconcentration followed by exponential clearance. Since the number ofimaging time-points typically collected in dosimetry studies would notresolve a dual parameter model (i.e., uptake and clearance rate), in oneembodiment, the methodology assumes that the total dose contributed bythe rising portion of a tissue or tumor time-activity curve is a smallfraction of the total absorbed dose delivered.

Equation (6) depends upon the tissue-specific intrinsic parameters, α, βand μ. These three parameters are set constant throughout a user-definedorgan or tumor volume. The voxel specific parameters are the total dosein a given voxel and the effective clearance half-life assigned to thevoxel. Given a voxel at coordinates (i,j,k), D^(ijk) and t_(e) ^(ijk)are the dose and effective clearance half-life for the voxel. Theimaging-based formulation of expression (6) that is incorporated into3D-RD is then:

$\begin{matrix}{{B\; E\; D^{ijk}} = {D^{ijk} + {\frac{\beta \; D^{{ijk}^{2}}}{\alpha}{\left( \frac{\ln (2)}{{\mu \cdot t_{e}^{ijk}} + {\ln (2)}} \right).}}}} & (7)\end{matrix}$

The user inputs values of α, β and μ for a particular volume and D^(ijk)and t_(e) ^(ijk) are obtained directly from the 3-D dose calculation andrate image, respectively. This approach requires organ or tumorsegmentation that corresponds to the different α, β and μ values. Thedose values are obtained by Monte Carlo calculation as describedpreviously, and the effective clearance half-lives are obtained byfitting the data to a single exponential function. Once a spatialdistribution of BED values has been obtained a dose-volume histogram ofthese values can be generated. Normalizing so that the total area underthe BED (differential) DVH curve is one, converts the BED DVH to aprobability distribution of BED values denoted, P(Ψ), where Ψ takes onall possible values of BED. Then, following the derivation for EUD asdescribed in O′Donoghue's Implications of Nonuniform Tumor Doses forRadioimmunotherapy, J Nucl Med., Volume 40, Issue 8, pages 1337-1341(1999), the EUD (1440) is obtained as:

$\begin{matrix}{{E\; U\; D} = {{- \frac{1}{\alpha}}{{\ln \left( {\int_{0}^{\infty}{{P(\psi)}^{{- \alpha}\; \psi}\ {\psi}}} \right)}.}}} & (8)\end{matrix}$

The EUD of the absorbed dose distribution (1465), as opposed to the BEDdistribution (1440), can also be obtained using equation (8), but usinga normalized DVH of absorbed dose values rather than BED values.Expression (8) may be derived by determining the absorbed dose requiredto yield a surviving fraction equal to that arising from the probabilitydistribution of dose values (absorbed dose or BED) given by thenormalized DVH.

A rigorous application of equation (7) would require estimation of theabsorbed dose at each time point (as in 1420); the resulting set ofabsorbed dose values for each voxel would then be used to estimate t_(c)^(ijk) (1425). In using activity-based rate images to obtain the t_(e)^(ijk), instead of the absorbed dose at each time point, the implicitassumption is being made that the local, voxel self-absorbed dosecontribution is substantially greater than the cross-voxel contribution.This assumption avoids the need to estimate absorbed dose at multipletime-points, thereby substantially reducing the time required to performthe calculation. In another embodiment of the invention absorbed doseimages at each time-point are generated and used for the BED calculation(1430), thereby avoiding the assumption regarding voxel self-dose vscross-dose contribution.

Radiobiological Parameters for Clearance Rate Effect Example

The illustrative simplified examples and also the clinicalimplementation involve dose estimation to lungs and to a thyroid tumor.Values of α and β for lung, and the constant of repair, μ, for eachtissue was taken from various sources. The parameter values are listedin the table in FIG. 21.

Clearance Rate Effect Example

As explained above, a sphere can be generated in a 563 matrix such thateach voxel represents a volume of (0.15 cm)³. All elements with acentroid greater than 1 cm and less than or equal to (2.0 cm) ⅓ from thematrix center (at 28,28,28) were given a clearance rate value (λ)corresponding to a half life of 2 hours. Those elements with a centerposition less than or equal to 1.0 cm from the center voxel wereassigned a λ value equivalent to a 4 hour half life. In this way anouter shell (with 2 hour half life) was separated from an inner sphere(with 4 hour half life) (FIG. 23). This allowed both regions to havenearly equivalent volumes. The procedure was used to generate a matrixrepresenting a sphere with a uniform absorbed dose distribution despitehaving non uniform clearance rate. This is accomplished by varying theinitial activity such that the cumulative activity of both regions isidentical. These two matrices were input into 3D-RD for the BED and EUDcalculations. Input of a dose distribution rather than an activitydistribution was necessary to make comparison with an analyticalcalculation possible. The partial-volume effects of a voxelized vs.idealized sphere were avoided by using the shell and sphere volumesobtained from the voxelized sphere rather than from a mathematicalsphere. The impact of sphere voxelization on voxel-based MC calculationshas been previously examined.

Absorbed Dose Distribution Effects. To demonstrate the impact of dosedistribution on EUD, the following model was evaluated (FIG. 24). First,a uniform density sphere (1.04 g/cc in both regions) was evaluated witha uniform absorbed dose distribution of 10 Gy. Second, the uniformsphere was divided into two equal volume regions. The inner sphere wasassigned zero absorbed dose while the outer shell was assigned anabsorbed dose of 20 Gy. The effective half-life was 2 hours in bothregions. Again the whole sphere average dose was 10 Gy.

Density Effects. To illustrate the effect of density differences, asphere with radius 1.26 cm was created that had unit cumulated activitythroughout, but a density of 2 g/cc in a central spherical region withradius 1 cm and 1 g/cc in the surrounding spherical shell. The inputparameters were chosen to yield a mean dose over the whole sphere of 10Gy. Since, for a constant spatial distribution of energy deposition, theabsorbed dose is a function of the density, the absorbed dose in thecenter is less than the absorbed dose of the shell. The distribution wasselected so that the average over the two regions was 10 Gy. 3D-RD wasused to generate a spatial distribution of absorbed dose values whichwere then used to estimate EUD over the whole sphere.

Application to a Patient Study

The 3D-RD dosimetry methodology was applied to an 11 year old femalethyroid cancer patient who has been previously described in apublication on MCNP-based 3D-ID dosimetry.

Imaging. SPECT/CT images were obtained at 27, 74, and 147 hours postinjection of a 37 MBq (1.0mCi) tracer 131I dose. All three SPECT/CTimages focused on the chest of the patient and close attention wasdirected at aligning the patient identically for each image. The imageswere acquired with a GE Millennium VG Hawkeye system with a 1.59 cmthick crystal.

An OS-EM based reconstruction scheme was used to improve quantization ofthe activity map. A total of 10 iterations with 24 subsets per iterationwas used. This reconstruction accounts for effects includingattenuation, patient scatter, and collimator response. Collimatorresponse includes septal penetration and scatter. The SPECT image countswere converted to units of activity by accounting for the detectorefficiency and acquisition time. This quantification procedure, combinedwith image alignment, made it possible to follow the kinetics of eachvoxel. Using the CTs, which were acquired with each SPECT, eachsubsequent SPECT and CT image was aligned to the 27 hour 3-D image set.A voxel by voxel fit to an exponential expression was then applied tothe aligned data set to obtain the clearance half-time for each voxel.

To obtain mean absorbed dose, mean BED and EUD, as well as absorbed doseand BED-volume-histograms, voxels were assigned to either tumor ornormal lung parenchyma using an activity threshold of 21% of highestactivity value.

Spherical Model Example

A spherical model was used to validate and illustrate the concepts ofBED and EUD.

Clearance Rate Effects. Assuming that the sphere was lung tissue andapplying the radiobiological parameters listed in the table of FIG. 21,the BED value in the slower clearing region, corresponding to the innersphere with an activity clearance half-life of 4 hours, was 13.14 Gy.The faster clearing region (outer shell, 2 hr half-life) yielded a BEDvalue of 15.69 Gy. The same model using the radiobiological values fortumor gave 10.09 Gy and 11.61 Gy for the slower clearing and fasterclearing regions, respectively. The mean absorbed dose (AD) value forall these regions was 10 Gy.

Absorbed Dose Distribution Effects. The EUD value over the whole spherewhen a uniform activity distribution was assumed recovered the meanabsorbed dose of 10 Gy. A non-uniform absorbed dose distribution wasapplied such that the inner sphere was assigned an absorbed dose ofzero, and an outer shell of equal volume, an absorbed dose of 20 Gy. Inthis case, the mean absorbed dose is 10 Gy, but the EUD was 1.83 Gy. Thesubstantially lower EUD value is no longer a quantity that may beobtained strictly on physics principles, but rather is dependent on theapplied biological model. The true absorbed dose has been adjusted toreflect the negligible probability of sterilizing all cells in a tumorvolume when half of the tumor volume receives an absorbed dose of zero.

Density Effects. In the sphere with non-uniform density (inner spheredensity of 2 g/cc, outer shell of equal volume (1 g/cc)) and an averageabsorbed dose of 10 Gy, the EUD over the whole sphere was 6.83 Gy. TheEUD value is lower than the absorbed dose value to reflect the dosenon-uniformity in spatial absorbed dose (inner sphere=5 Gy, outershell=15 Gy) arising from the density differences.

Application to a Patient Study. A 3D-RD calculation was performed forthe clinical case described in the methods. A dosimetric analysis forthis patient, without the radiobiological modeling described in thiswork has been previously published using the Monte Carlo code MCNP asopposed to EGSnrc which was used in this work. The clinical exampleillustrates all of the elements investigated using the simple sphericalgeometry. As shown on the CT scan (FIG. 26 a), there is a highlyvariable density distribution in the lungs due to the tumor infiltrationof normal lung parenchyma. Coupled with the low lung density, this givesa density and tissue composition that includes air, lung parenchyma andtumor (which was modeled as soft tissue). As shown on FIGS. 26 b and 26c, the activity and clearance kinetics of 131I are also variable overthe lung volume. These two data sets were used to calculate thecumulated activity images shown in FIG. 26 d.

A comparison between the EGS-based 3D-RD calculation and the previouslypublished MCNP-based calculation was performed. FIG. 27 depicts the DVHof the absorbed dose distribution obtained with 3D-RD superimposed onthe same plot as the previously published DVH. Good overall agreementbetween the two DVHs is observed and the mean absorbed doses, expressedas absorbed dose per unit cumulated activity in the lung volume are ingood agreement, 3.01×10-5 and 2.88×10-5 mGy/MBq-s per voxel, for thepublished, MCNP-based, and 3D-RD values, respectively.

FIGS. 28 and 29 depict the results obtained with the radiobiologicalmodeling capabilities of 3D-RD. FIG. 28 depicts a parametric image ofBED values. Within this image the spotty areas of highest dose are areaswhere high activity and low density overlap. In FIG. 29 a, normalized(so that the area under the curve is equal to 1) DVH and BED DVH (BVH)are shown for tumor voxels. The near superimposition of DVH and BVHsuggests that dose rate will have a minimal impact on tumor response inthis case. FIG. 29 b depicts the normalized BVH for normal lungparenchyma. The DVH and BVH are given in Gy and reflect the predicteddoses resulting from the administered therapeutic activity of 1.32 GBq(35.6 mCi) of 131I. These plots may be used to derive EUD values. It isimportant to note that the volume histograms must reflect the actualabsorbed dose delivered and not the dose per unit administered activity.This is because the EUD is a nonlinear function of absorbed dose. Themodel relies on estimation of a tumor control probability to yield theequivalent uniform dose. If the data used to estimate EUD are expressedas dose per administered activity the EUD value will be incorrect. Meanabsorbed dose, mean BED, and EUD are summarized in table 2. The EUDvalue for tumor, which accounts for the effect of a non-uniform dosedistribution, was approximately 43% of the mean absorbed dose. Thisreduction brings the absorbed dose to a range that is not likely to leadto a complete response. The analysis demonstrates the impact of dosenon-uniformity on the potential efficacy of a treatment.

CONCLUSION

While various embodiments have been described above, it should beunderstood that they have been presented by way of example, and notlimitation. It will be apparent to persons skilled in the relevantart(s) that various changes in form and detail can be made thereinwithout departing from the spirit and scope. In fact, after reading theabove description, it will be apparent to one skilled in the relevantart(s) how to implement alternative embodiments. Thus, the presentembodiments should not be limited by any of the above describedexemplary embodiments.

In addition, it should be understood that any figures which highlightthe functionality and advantages, are presented for example purposesonly. The disclosed architecture is sufficiently flexible andconfigurable, such that it may be utilized in ways other than thatshown. For example, the steps listed in any flowchart may be re-orderedor only optionally used in some embodiments.

Further, the purpose of the Abstract of the Disclosure is to enable theU.S. Patent and Trademark Office and the public generally, andespecially the scientists, engineers and practitioners in the art whoare not familiar with patent or legal terms or phraseology, to determinequickly from a cursory inspection the nature and essence of thetechnical disclosure of the application. The Abstract of the Disclosureis not intended to be limiting as to the scope in any way.

Finally, it is the applicant's intent that only claims that include theexpress language “means for” or “step for” be interpreted under 35U.S.C. 112, paragraph 6. Claims that do not expressly include the phrase“means for” or “step for” are not to be interpreted under 35 U.S.C. 112,paragraph 6.

1. A computerized method for determining an optimum amount ofradioactivity to administer to a patient, comprising: assuming anactivity retention limit; utilizing the activity retention limit todetermine a dose rate for a phantom category; utilizing the dose ratefor the phantom category to determine the dose rate for a second phantomcategory; and utilizing the dose rate for a second phantom category tofind information regarding the second phantom category.
 2. The method ofclaim 1, wherein the information is the activity retention limit for thesecond phantom category.
 3. The method of claim 1, further comprising:obtaining the mean absorbed dose by integrating the dose rate over time;using the mean absorbed dose to determine an optimum amount ofradioactivity to administer to the patient.
 4. The method of claim 1,wherein a dose rate resulting from short range particulate emissions isdistinguished from a dose rate resulting from longer range emissions. 5.The method of claim 4, wherein the short range particulate emissions areelectrons.
 6. The method of claim 4, wherein the longer range emissionsare photons.
 7. The method of claim 1, wherein utilizing the activityretention limit to determine the dose rate for the phantom categoryfurther comprises calculating how the dose rate is related to theactivity retention limit in a particular point in time.
 8. The method ofclaim 1, wherein utilizing the activity retention limit to determine thedose rate for the phantom category further comprises using the followingformula:DR ^(P)(t)=A _(LU)(t)·S _(LU←LU) ^(P) +A _(RB)(t)·S _(LU←RB) ^(P)  (1),with: $\begin{matrix}{{{A_{LU}(t)} = {\frac{A_{T} \cdot F_{T}}{^{{- \lambda_{LU}} \cdot T}}^{{- \lambda_{LU}} \cdot t}}},} & (2) \\{{{A_{RB}(t)} = {\frac{A_{T} \cdot \left( {1 - F_{T}} \right)}{^{{- \lambda_{RB}} \cdot T}}^{{- \lambda_{RB}} \cdot t}}},} & (3) \\{{S_{{LU}\leftarrow{RB}}^{P} = {{S_{{LU}\leftarrow{TB}}^{P} \cdot \frac{M_{TB}^{P}}{\left( {M_{TB}^{P} - M_{LU}^{P}} \right)}} - {S_{{LU}\leftarrow{LU}}^{P} \cdot \frac{M_{LU}^{P}}{\left( {M_{TB}^{P} - M_{LU}^{P}} \right)}}}},} & (4)\end{matrix}$ A_(LU)(t) lung activity at time t,| S_(LU←LU) ^(P) lung tolung ¹³¹I S-factor for reference phantom, P, A_(RB)(t) remainder bodyactivity (total-body-lung) at time, t, S_(LU←RB) ^(P) remainder body tohung ¹³¹I S-factor for reference phantom, P. A_(T) whole-body activityat time, T, F_(T) fraction of A_(T) that is in the lungs at time, T,λ_(LU) effective clearance rate from lungs (=ln(2)/T_(E), withT_(E)=effective half-life), λRB effective clearance rate from remainderbody (=ln(2)/T_(RB), with T_(RB)=effective half-life in remainder body),S_(LU←TB) ^(P) total-body to lung ¹³¹I S-factor for reference phantom.P, M_(TB) ^(P) total-body mass of reference phantom. P, M_(LU) ^(P) lungmass of reference phantom, P.
 9. The method of claim 3, whereinobtaining the mean absorbed dose by integrating the dose rate over timefurther comprises utilizing the following formula:DLU=Ã _(LU) ·S _(LU←LU) ^(P) +Ã _(RB) ·S _(LU←RB) ^(P)  (9). with$\begin{matrix}{{{\overset{\sim}{A}}_{LU} = {\frac{A_{DRC}^{P} \cdot F_{48} \cdot ^{\frac{\ln {(2)}}{T_{E}}T}}{\ln (2)} \cdot T_{E}}},} & (10) \\{{\overset{\sim}{A}}_{RB} = {\frac{A_{DRC}^{P} \cdot \left( {1 - F_{48}} \right) \cdot ^{\frac{\ln {(2)}}{T_{RB}} \cdot T}}{\ln (2)} \cdot {T_{RB}.}}} & (11)\end{matrix}$
 10. A computerized method for determining an optimumamount of radioactivity to administer to a patient, comprising:obtaining at least one image relating to anatomy of a particularpatient; obtaining multiple images regarding radioactivity distributionover time in the particular patient; registering the images related tothe radioactivity distribution over time; combining each radioactivityimage with each anatomy image to create an activity image; running aMonte Carlo simulation for each activity image to obtain a dose image atmultiple times; using the dose image at each time to obtain a dose-rateimage and a total dose image; using the dose-rate image and total doseimage to obtain a BED image; using the BED image to obtain an EUD of BEDvalues for a chosen anatomical region.
 11. The method of claim 10,wherein the BED is depicted as a frequency of occurrence of a particularBED.
 12. The method of 11, wherein the particular total dose image isdepicted as: a differential BED histogram; an integral BED histogram; oriso BED contours over the image; or any combination thereof.
 13. Themethod of claim 10, wherein the BED value for each voxel is obtainedfrom an individual voxel dose value and an individual voxel dose-rateparameter value or by a voxel dose-rate half-time value.
 14. The methodof claim 10, wherein the following equation is used to obtain the BEDfor each voxel given a voxel dose D^(ijk), and a voxel dose-rateparameter value (or equivalently the voxel dose-rate half-time) t_(e)^(ijk): $\begin{matrix}{{B\; E\; D^{ijk}} = {D^{ijk} + {\frac{\beta \; D^{{ijk}^{2}}}{\alpha}{\left( \frac{\ln (2)}{{\mu \cdot t_{e}^{ijk}} + {\ln (2)}} \right).}}}} & (7)\end{matrix}$
 15. A computerized method for determining an optimumamount of radioactivity to administer to a patient, comprising:obtaining at least one image relating to anatomy of a particularpatient; obtaining multiple images regarding radioactivity distributionover time in the particular patient; registering the images related tothe radioactivity distribution over time; integrating the radioactivityimages across time voxel-wise to obtain a cumulated activity image;combining the cumulative activity image with the anatomy image toestablish a corresponding set of images representing the cumulatedactivity in each voxel and the corresponding density and composition forthe voxel; running a Monte Carlo simulation for each set of images toobtain a total dose image; and using the total dose image to obtain theEUD of dose value for a user-defined region.
 16. The method of claim 15,wherein the total dose image is depicted as a frequency of occurrence ofa particular total dose value.
 17. The method of claim 16, wherein theparticular total dose image is depicted: a differential dose volumehistogram; an integral dose volume histogram; or iso dose contours overthe image; or any combination thereof.
 18. A computerized system fordetermining an optimum amount of radioactivity to administer to apatient, comprising: a server coupled to a network; a user terminalcoupled to the network; an application coupled to the server and/or theuser terminal, wherein the application is configured for: assuming anactivity retention limit; utilizing the activity retention limit todetermine a dose rate for a phantom category; utilizing the dose ratefor the phantom category to determine the dose rate for a second phantomcategory; and utilizing the dose rate for a second phantom category tofind information regarding the second phantom category.
 19. The systemof claim 18, wherein the information is the activity retention limit forthe second phantom category.
 20. The system of claim 18, wherein theapplication is further configured for: obtaining the mean absorbed doseby integrating the dose rate over time; using the mean absorbed dose todetermine an optimum amount of radioactivity to administer to thepatient.
 21. The system of claim 18, wherein a dose rate resulting fromshort range particulate emissions is distinguished from a dose rateresulting from longer range emissions.
 22. The system of claim 21,wherein the short range particulate emissions are electrons.
 23. Thesystem of claim 21, wherein the longer range emissions are photons. 24.The system of claim 18, wherein utilizing the activity retention limitto determine the dose rate for the phantom category further comprisescalculating how the dose rate is related to the activity retention limitin a particular point in time.
 25. The system of claim 18, whereinutilizing the activity retention limit to determine the dose rate forthe phantom category further comprises using the following formula:DR ^(P)(t)=A _(LU)(t)·S _(LU←LU) ^(P) +A _(RB)(t)·S _(LU←RB) ^(P)  (1),with: $\begin{matrix}{{{A_{LU}(t)} = {\frac{A_{T} \cdot F_{T}}{^{{- \lambda_{LU}} \cdot T}}^{{- \lambda_{LU}} \cdot t}}},} & (2) \\{{{A_{RB}(t)} = {\frac{A_{T} \cdot \left( {1 - F_{T}} \right)}{^{{- \lambda_{RB}} \cdot T}}^{{- \lambda_{RB}} \cdot t}}},} & (3) \\{{S_{{LU}\leftarrow{RB}}^{P} = {{S_{{LU}\leftarrow{TB}}^{P} \cdot \frac{M_{TB}^{P}}{\left( {M_{TB}^{P} - M_{LU}^{P}} \right)}} - {S_{{LU}\leftarrow{LU}}^{P} \cdot \frac{M_{LU}^{P}}{\left( {M_{TB}^{P} - M_{LU}^{P}} \right)}}}},} & (4)\end{matrix}$ A_(LU)(t) lung activity at time t,| S_(LU←LU) ^(P) lung tolung ¹³¹I S-factor for reference phantom, P, A_(RB)(t) remainder bodyactivity (total-body-lung) at time, t, S_(LU←RB) ^(P) remainder body tohung ¹³¹I S-factor for reference phantom, P, A_(T) whole-body activityat time, T, F_(T) fraction of A_(T) that is in the lungs at time, T,λ_(LU) effective clearance rate from lungs (=ln(2)/T_(E); withT_(E)=effective half-life), λRB effective clearance rate from remainderbody (=ln(2)/T_(RB), with T_(RB)=effective half-life in remainder body),S_(LU←TB) ^(P) total-body to lung ¹³¹I S-factor for reference phantom.P, M_(TB) ^(P) total-body mass of reference phantom, P, M_(LU) ^(P) lungmass of reference phantom, P.
 26. The method of claim 20, whereinobtaining the mean absorbed dose by integrating the dose rate over timefurther comprises utilizing the following formula:DLU=Ã _(LU) ·S _(LU←LU) ^(P) +Ã _(RB) ·S _(LU←RB) ^(P)  (9). with$\begin{matrix}{{{\overset{\sim}{A}}_{LU} = {\frac{A_{DRC}^{P} \cdot F_{48} \cdot ^{\frac{\ln {(2)}}{T_{E}}T}}{\ln (2)} \cdot T_{E}}},} & (10) \\{{\overset{\sim}{A}}_{RB} = {\frac{A_{DRC}^{P} \cdot \left( {1 - F_{48}} \right) \cdot ^{\frac{\ln {(2)}}{T_{RB}} \cdot T}}{\ln (2)} \cdot {T_{RB}.}}} & (11)\end{matrix}$
 27. A computerized system for determining an optimumamount of radioactivity to administer to a patient, comprising: a servercoupled to a network; a user terminal coupled to the network; anapplication coupled to the server and/or the user terminal, wherein theapplication is configured for: obtaining at least one image relating toanatomy of a particular patient; obtaining multiple images regardingradioactivity distribution over time in the particular patient;registering the images related to the radioactivity distribution overtime; combining each radioactivity image with each anatomy image tocreate an activity image; running a Monte Carlo simulation for eachactivity image to obtain a dose image at multiple times; using the doseimage at each time to obtain a dose-rate image and a total dose image;using the dose-rate image and total dose image to obtain a BED image;using the BED image to obtain an EUD of BED values for a chosenanatomical region.
 28. The system of claim 27, wherein the BED isdepicted as a frequency of occurrence of a particular BED.
 29. Thesystem of claim 28, wherein the particular total dose image is depictedas: a differential BED histogram; an integral BED histogram; or iso BEDcontours over the image; or any combination thereof.
 30. The system ofclaim 27, wherein the BED value for each voxel is obtained from anindividual voxel dose value and an individual voxel dose-rate parametervalue or by a voxel dose-rate half-time value.
 31. The system of claim27, wherein the following equation is used to obtain the BED for eachvoxel given a voxel dose D^(ijk), and a voxel dose-rate parameter value(or equivalently the voxel dose-rate half-time) t_(e) ^(ijk):$\begin{matrix}{{B\; E\; D^{ijk}} = {D^{ijk} + {\frac{\beta \; D^{{ijk}^{2}}}{\alpha}{\left( \frac{\ln (2)}{{\mu \cdot t_{e}^{ijk}} + {\ln (2)}} \right).}}}} & (7)\end{matrix}$
 32. A computerized system for determining an optimumamount of radioactivity to administer to a patient, comprising: a servercoupled to a network; a user terminal coupled to the network; anapplication coupled to the server and/or the user terminal, wherein theapplication is configured for: obtaining at least one image relating toanatomy of a particular patient; obtaining multiple images regardingradioactivity distribution over time in the particular patient;registering the images related to the radioactivity distribution overtime; integrating the radioactivity images across time voxel-wise toobtain a cumulated activity image; combining the cumulative activityimage with the anatomy image to establish a corresponding set of imagesrepresenting the cumulated activity in each voxel and the correspondingdensity and composition for the voxel; running a Monte Carlo simulationfor each set of images to obtain a total dose image; and using the totaldose image to obtain the EUD of dose value for a user-defined region.33. The system of claim 32, wherein the total dose image is depicted asa frequency of occurrence of a particular total dose value.
 34. Thesystem of claim 33, wherein the particular total dose image is depicted:a differential dose volume histogram; an integral dose volume histogram;or iso dose contours over the image; or any combination thereof.